This paper presents an algorithm to determine whether a stochastic matrix is regular. The main theorem is the following. Hypothesis: An n-by-n stochastic matrix has at least one positive entry off the main diagonal in every row and column. There is at most one row with n — 1 zeros and at most one column with n — 1 zeros. There are no j-by-k submatrices consisting entirely of zeros, where j and k are integers greater than 1, with j + k = n. Conclusion: The matrix is regular. Similar results hold for strongly connected digraphs.
